{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3XEI46MBB7OHUHA6G6UASKBNGR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9b00cfab35bd01473e463c289bcf96f60893583c0f1ae24c58e0bc089bc012a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-16T07:52:33Z","title_canon_sha256":"867fb0de68ea42ed200ba036d1bfb6ac61108d93c4b91b657cc6fa3fe1529c4b"},"schema_version":"1.0","source":{"id":"1104.3204","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3204","created_at":"2026-05-18T04:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3204v2","created_at":"2026-05-18T04:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3204","created_at":"2026-05-18T04:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"3XEI46MBB7OH","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3XEI46MBB7OHUHA6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3XEI46MB","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:0491577c17ad140ff7fe0864842cdc97137f79c49d9622dd724b65355e77d888","target":"graph","created_at":"2026-05-18T04:15:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this note, we obtain the asymptotic estimate for the time derivative of the $\\Phi$-entropy in terms of the lower bound on the Bakry-Emery $\\Gamma_2$ curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the $\\Phi$-entropy is non-increasing, and we also get sharp asymptotic bound for the time derivative of the entropy in the Heisenberg group.","authors_text":"Bin Qian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-16T07:52:33Z","title":"Asymptotic estimates on the time derivative of $\\Phi$-entropy on Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3204","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d239bc50618fe6da9b21d790724487936aa20c933981da92152399f724fa40c2","target":"record","created_at":"2026-05-18T04:15:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9b00cfab35bd01473e463c289bcf96f60893583c0f1ae24c58e0bc089bc012a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-16T07:52:33Z","title_canon_sha256":"867fb0de68ea42ed200ba036d1bfb6ac61108d93c4b91b657cc6fa3fe1529c4b"},"schema_version":"1.0","source":{"id":"1104.3204","kind":"arxiv","version":2}},"canonical_sha256":"ddc88e79810fdc7a1c1e37a809282d347b10df30d3e4640608881fac9f398acf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddc88e79810fdc7a1c1e37a809282d347b10df30d3e4640608881fac9f398acf","first_computed_at":"2026-05-18T04:15:38.882586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:38.882586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MSr5Mablp3kJ6MsxnMSsPWOPr+EFFMZYiBeqngmgB3CEzbqx8nBv4TNThpeCGS2c2Y1nZE0MbBZO1y+jhZeOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:38.883488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3204","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d239bc50618fe6da9b21d790724487936aa20c933981da92152399f724fa40c2","sha256:0491577c17ad140ff7fe0864842cdc97137f79c49d9622dd724b65355e77d888"],"state_sha256":"a44b89a35ff51cd14b15525914d066c5d0d80cf81c841f91a750a46d02a3c54b"}